Optically uniaxial materials are commonly used to change the polarization of light. It is well known that optically uniaxial materials operate according to the principle of optical asymmetry--meaning that an electric field oriented along one axis of an optically uniaxial material experiences a dielectric response or refraction index that is different from that of a field oriented along one or both of the other two. The unique axis is known as the extraordinary axis, or optical axis. The other two axes are known as the ordinary axes.
If a light wave incident on optically uniaxial material has electric field components both parallel and perpendicular to the optical axis, the uniaxial material has the effect of changing the relative phase of the components. This slowing of one polarization component relative to the other polarization component is known as "retardation".
A wave plate is a cut slice of optically uniaxial material, usually an optically uniaxial crystal. As is discussed in greater detail below, ideally one would prefer a wave plate where the retardation is less than one wavelength. Such a wave plate is known as a "zero-order" wave plate. Unfortunately, for ultraviolet applications, a zero-order plate made of suitable material would be so thin that it would be virtually impossible, if not impossible, to fabricate.
In some applications, therefore, a multiple-order wave plate is used as a substitute. A multiple-order wave plate operates on the principle that waves repeat themselves every 360 degrees. Therefore, a phase retardation of x+n*360 degrees (where "n" is an integer) is theoretically the same as a phase retardation of x degrees. Unfortunately, multiple-order wave plates have practical disadvantages when compared to zero-order wave plates. One disadvantage is that multiple-order wave plates are much more sensitive to wavelength than zero-order wave plates. Another disadvantage is that the retardation of a multiple-order wave plate is also more sensitive to changes in the angle of incidence of the incident light wave.
It is known that a zero-order wave plate can be constructed from two multiple-order plates of slightly different thicknesses if the extraordinary axis of one is oriented parallel to the ordinary axis of the other. In some configurations, e.g. the Babinet-Soleil compensator, one of the two plates is actually two wedge-shaped pieces such that the effective thickness can be changed by changing their overlap. Thus, some or all of the phase difference caused by the light travelling through the first plate can be cancelled out as the light travels through the second plate. A disadvantage of such "biplate" retarders is that not only do they require two or more elements, but also that the two elements must be aligned very carefully.
It is also known that a compensator can be constructed from a single plate of uniaxial material. (The term "compensator" is used in the art to refer to a retarder whose retardation is adjustable, usually continuously adjustable.) This plate, a Berek's compensator, is a single planar plate of a uniaxial crystal cut such that the extraordinary axis is perpendicular to the plane of the plate. As shown in FIG. 1A, a light beam 102 incident to the plate 104 at normal (90.degree.) incidence travels along the extraordinary axis and therefore for any polarization the electric field experiences the ordinary refractive index, hence no component is phase retarded relative to any other component. Put another way, the velocity of the normally incident light beam 102 through the Berek's compensator 104 is independent of polarization. As shown in FIG. 1B, in operation, to introduce a relative retardation in one of the components, the plate 104 is tilted (for example, by the angle .THETA..sub.T) so that one of the field components (denoted in FIG. 1B as n.sub.c ') becomes slightly extraordinary. The amount of phase retardation of the output beam 156 relative to the input beam 152 is a function of the angle .THETA..sub.T of tilt.
While Berek's compensators eliminate many of the disadvantages of biplate retarders, they do however have their own disadvantages. One disadvantage is that the crystal must be mechanically tilted to achieve the desired retardation, which requires precision mechanical control. Tilting is particularly difficult when it is also required that the tilted compensator be rotated, such as in an ellipsometer where the compensator is rotated (see below). For example, in such an ellipsometer, the compensator of FIG. 1B may be rotated as denoted by the arrow 158 about the axis defined by the direction of the incident light beam. A further disadvantage of the conventional Berek's compensator is that, in use, the incident light beam is not normally incident (i.e. 90 degrees) to the plate (such as light beam 102 shown in FIG. 1A), so the light beam changes direction at the input air/plate interface (as indicated by beam 155 in FIG. 1B) and at the output plate/air interface due to the difference in refractive index between the air and the plate. This direction change is governed by the well-known Snell's law. So long as the input face of the Berek's compensator is parallel to the output face of the Berek's compensator (for example, as are the faces of the plate 104 shown in FIGS. 1A and 1B), then the direction of the output beam (denoted by reference numeral 106 in FIG. 1A, and by reference numeral 156 in FIG. 1B) is the same as that of the input beam (102 and 152, respectively). This is because, in accordance with Snell's law, whatever angle of direction change occurs at the input face (the light beam within the compensator 104 is denoted in FIG. 1B by reference numeral 155) is reversed at the parallel output face. However, even though there is no difference in direction between the output beam 156 and the input beam 152, the difference in the index of refraction between the Berek's compensator 104 and the air causes the output beam 156 to be displaced laterally from-the input beam 152.
One application in which compensator operation is important is optical ellipsometry. Optical ellipsometry has long been recognized as being a non-destructive technique to provide accurate characterizations of semiconductors and other materials, their surface conditions, layer compositions and thicknesses, and for characterizing overlying oxide layers. This technique is particularly useful to evaluate thickness, crystallinity, composition and index of refraction characteristics of thin films deposited on semiconductor or metal substrates to ensure high yields during fabrication.
By way of background, an ellipsometer probes a sample with a light beam having a known polarization state. The light beam is reflected at non-normal incidence from the surface of the sample. The polarization state of the beam is modified upon reflection in a way that depends upon the properties of the sample. By accurately measuring the polarization state of the reflected beam and comparing it to the original polarization state, various properties of the sample can be ascertained.
In spectroscopic ellipsometry, the probing wavelength is changed and the ellipsometric measurement is repeated at each new wavelength. Spectroscopic ellipsometry is ideal for multi-material samples formed in stacked layers. The different depth penetrations and spectral responses that depend on the material and wavelength of light provide additional information about a sample that is not available from single wavelength ellipsometers.
Many configurations have been proposed to measure the change in polarization state that occurs upon reflection. In one type of ellipsometer only two optical elements are used, a polarizer and an analyzer, one of which is held fixed and the other rotated. Such an ellipsometer, commonly called a rotating-polarizer or rotating-analyzer ellipsometer, is termed "an incomplete" polarimeter, because it is insensitive to the handedness of the circularly polarized component and exhibits poor performance when the light being analyzed is either nearly completely linearly polarized or possesses a depolarized component.
The latter limitations of the rotating-polarizer and rotating-analyzer ellipsometers can be overcome by including a rotatable compensator placed between the polarizer and the analyzer, both of which are now fixed. The compensator can be placed either between the sample and the polarizer, or between the sample and the analyzer. Such a configuration is commonly called a rotatable compensator ellipsometer.
For the purposes of this patent application, a rotatable compensator ellipsometer should be thought of as being generally one at least of two types. With the first type, the compensator is rotated incrementally and stopped at each incremental angle, and data are obtained while the compensator is stationary. With the other type, the compensator is rotated substantially continuously and data are obtained while the compensator is moving. With this latter type of compensator, the obtained data are typically corrected for the averaging that occurs as a result of the compensator moving during a data-acquisition interval.
As discussed above in some detail, the compensator is an optical component that delays the light polarized parallel to its slow axis relative to light polarized parallel to its fast axis by an amount proportional to the refractive index difference along the two directions and the thickness of the plate, and inversely proportional to the wavelength of the light.
Unfortunately, as also discussed above, conventional compensators have characteristics that make them difficult to use, or that make it more difficult to obtain precise results. For example, the displacement phenomena of Berek's compensators causes a light beam passed through the rotatable compensator of an ellipsometer to rotate in a circle along with the compensator. Therefore, what is desired, particularly for use in optical ellipsometry but not necessarily limited to this application, is a compensator that is relatively uncomplicated to operate and does not detract from the accuracy of the ellipsometry results.